A052764 E.g.f.: -1/4*LambertW(-4*x).

0, 1, 8, 144, 4096, 160000, 7962624, 481890304, 34359738368, 2821109907456, 262144000000000, 27197360938418176, 3116402981210161152, 390877006486250192896, 53265296773103187132416, 7836416409600000000000000, 1237940039285380274899124224, 208998227690370098316628197376

Offset

0,3

Comments

Previous name was: A simple grammar.

Links

G. C. Greubel, Table of n, a(n) for n = 0..320

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 721

Formula

E.g.f.: -1/4*LambertW(-4*x).

For n>0, a(n) = 2^(2*n-2)*n^(n-1). - Vaclav Kotesovec, Sep 30 2013

a(n) = [x^n] x/(1 - 4*n*x). - Ilya Gutkovskiy, Oct 12 2017

Maple

spec := [S, {B=Set(S), S=Prod(Z, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

CoefficientList[Series[-1/4*LambertW[-4*x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace((-1/4)*lambertw(-4*x)))) \\ G. C. Greubel, Nov 07 2017

Crossrefs

Sequence in context: A067421 A124059 A275867 * A341957 A024284 A024285

Adjacent sequences: A052761 A052762 A052763 * A052765 A052766 A052767

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

New name using e.g.f. by Vaclav Kotesovec, Sep 30 2013

Status

approved